Geometry of δ-almost gradient Yamabe solitons on pseudo-Riemannian manifolds

Abstract

In this article, we studied δ-almost Yamabe solitons within the framework of para- contact metric manifolds. First, we proved that for a paracontact metric manifold {M}, if a paracontact metric g represents a δ-almost Yamabe soliton associated with the potential vector field {Z} being an infinitesimal contact transformation, then {Z} is Killing and if the potential vector field {Z} is collinear with ξ, then the manifold {M} is {K}-paracontact. Next, if we take a {K}-paracontact metric mani- fold admitting δ-almost Yamabe soliton with the potential vector field {Z} parallel to the characteristic vector field and with constant scalar curvature then either scalar curvature will vanish or {g} becomes a δ-Yamabe soliton under a certain condition. We established some results on {K}-paracontact manifold admitting δ-almost gradient Yamabe soliton. Moreover, we consider a (k, μ)-paracontact metric manifold admitting a non-trivial δ-almost gradient Yamabe soliton. We shown that the potential vector field Z is parallel to ξ. We have also discussed about δ-almost gradient Yamabe soliton on the para-Sasakian manifold. Finally, we consider a para-cosymplectic manifold with a δ-almost Yamabe soliton. In the end, we construct two examples of K-paracontact metric manifolds with δ-almost Yamabe soliton.